Question

How would one determine the amplitude period and phase and vertical shift of a sin wave here's an exapmle to work with 4cos2/3 X

Answer 1

amplitude is the value of the displacement when the function is at its maximum - so when can "4cos(2x/3)" - rather what is it's maximum value?

Answer 2

4

Answer 3

and would the period be 2/3?

Answer 4

yeah. right that's the maximum of the displacement function, so amplitude is gonna be '4'

Now, think about the argument of 'cos'. - it's 2x/3 right in this case right?

Now when cosX is given, it's period is 2pi - right? That is, the cosX curve repeats itself every 2pi distance, so when would the cos(2x/3) curve start repeating itself then?

Answer 5

every 1/4pi?

Answer 6

umm.. no.

Actually, let's do it this way-

If X--->2pi, then
2/3x --->??

unitary method remember??